You can fake your death by any method that doesn't leave a body, which leaves out any suicide that puts your body in the coroner's hands. And without a body, I imagine you couldn't get a legal assertion of suicide.
Fictional drugs that create the illusion of death have been around since Romeo and Juliet and before, no doubt. I don't know of any real drugs that would do this trick. Have the narcoleptic ever really been taken for dead, as in "The Premature Burial"? Don't know again, but fiction has jumped on the idea often enough.
Drowning is good because given a big enough body of water and/or the right conditions, searchers could miss a body and give up the hunt.
Death by exposure (or foul play) in the wilderness is another good way to fake your demise -- again, given enough wilderness, searchers could credibly hunt in vain. Sometimes it takes months to find a body hidden even in a small band of parkland -- there was an infamous case in Washington, DC not long ago, wasn't there?
You could be assumed dead if you disappeared for long enough. Maybe the assumption of death is all the "dead" character would need. If the character must be declared legally dead, you'd have to research what evidence or what passage of time would satisfy local law.